The first problem was easy enough to diagnose. Since I had rebuilt and rewired the circuit it had to be the thermistor itself. After removing it, I could see the underside was looking a bit toasted. I don't think it was designed for use up to 250°C. The insulation on the wire was not up to it and I suspect it was soldered to the actual device, and that the solder melted. There seems to be some solder on the brass nozzle now where it was mounted.
The remedy was easy: I just replaced it with the recommended glass bead thermistor which had arrived from back order in the meantime. It is rated to 300°C. Its characteristics are different so I had to change my resistor values, but I had anticipated that by mounting them on the connector rather than the board.